English

On a Characterization of the Rellich-Kondrachov Theorem on Groups

Analysis of PDEs 2022-06-07 v1

Abstract

Motivated by an eigenvalue-eigenfunction problem posed in IR^n x {\Omega}, where {\Omega} is a probability space, we are concerned in this paper with the Sobolev space on groups. Hence it is established an equivalence between locally compact Abelian groups and the space of solutions to the associated variational problem. Then, we study some conditions which characterize in a precisely manner the Rellich-Kondrachov Theorem, the principal ingredient to solve the variational problem.

Keywords

Cite

@article{arxiv.2206.02726,
  title  = {On a Characterization of the Rellich-Kondrachov Theorem on Groups},
  author = {Vernny Ccajma and Wladimir Neves and Jean Silva},
  journal= {arXiv preprint arXiv:2206.02726},
  year   = {2022}
}

Comments

25 pages. arXiv admin note: text overlap with arXiv:2101.11338